The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

This problem trains for: SAT-I, AMC-8, GMAT.

If x≠0 and x≠3, the algebraic expressions:

and

are of different signs when:

Whatever the value of x, the factors are the same in both expressions. Since the rule of signs is the same for multiplication as for division, the expressions have the same sign regardless of the value of x.